arXiv subjects

Felix Schmäschke

Publications and source records attributed to Felix Schmäschke.

4 recordsLinked to original sources

arXiv2024

Trisecting a 4-dimensional book into three chapters

We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algorithm also works for open books on manifolds with non-empty boundary and for 3-manifold bundles over the circle. We apply this algorithm to several simple open books, demonstrate that it is compatible with various topological constructions, and argue that it generalizes and unifies several previously known constructions.

math.GT↗

arXiv2017

On geodesic flows with symmetries and closed magnetic geodesics on orbifolds

Let $Q$ be a closed manifold admitting a locally-free action of a compact Lie group $G$. In this paper we study the properties of geodesic flows on $Q$ given by Riemannian metrics which are invariant by such an action. In particular, we will be interested in the existence of geodesics which are closed up to the action of some element in the group $G$, since they project to closed magnetic geodesics on the quotient orbifold $Q/G$.

math.DS↗

arXiv2017

On the existence of closed magnetic geodesics via symplectic reduction

Let $(M,g)$ be a closed Riemannian manifold and $σ$ be a closed 2-form on $M$ representing an integer cohomology class. In this paper, using symplectic reduction, we show how the problem of existence of closed magnetic geodesics for the magnetic flow of the pair $(g,σ)$ can be interpreted as a critical point problem for a Rabinowitz-type action functional defined on the cotangent bundle $T^*E$ of a suitable $S^1$-bundle $E$ over $M$ or, equivalently, as a critical point problem for a Lagrangian-type action functional defined on the free loopspace of $E$. We then study the relation between the stability property of energy hypersurfaces in $(T^*M,dp\wedge dq+π^*σ)$ and of the corresponding codimension 2 coisotropic submanifolds in $(T^*E,dp\wedge dq)$ arising via symplectic reduction. Finally, we reprove the main result of [9] in this setting.

math.DS↗

arXiv2016

Floer homology of Lagrangians in clean intersection

We consider Floer homology associated to a pair of closed Lagrangian submanifolds that satisfy a monotonicty assumption. If the Lagrangians intersect cleanly we decribe two spectral sequences which help to compute their Floer homology. The spectral sequences are constructed using a Morse-Bott version of Floer homology. We give a full treatment of the theory including orientations.

math.SG↗